When lyricist Howard Ashman died at 40 on March 14 of AIDS-related complications in New York, he had only just started upon a musical career that might have rivaled the best. In 1982, Ashman and composer Alan Menken redefined Off Broadway theater with Little Shop of Horrors, the unexpected hit (and '86 film) about a carnivorous houseplant. Last year the team won an Oscar for the rowdy calypso song, The Little Mermaid's ''Under the Sea.'' They'd completed work on two more animated features for Disney, Beauty and the Beast, coming in November, and next year's Aladdin. Those who knew Ashman call him ''tough'' but he was most at home in songs about lonely dreamers. ''Working with a fairy tale,'' he said after Mermaid, ''you do a different kind of dreaming.''